There is no reason, necessarily, that DAI would be worth more than 1$ just because ETH drops. In fact it may be worth less than $1 not only because of supply and demand factors but because of the increased risk that it becomes undercollateralized.

You could absolutely have market conditions where people want no part of DAI or ETH, and then it becomes an imbalance (if the amount of DAI is large).

It is very similar to what happens with SBD.

Also, SBD isn't created out of nothing. It is converted from STEEM in the reward pool. It is the STEEM in the reward pool that is created out of nothing (inflation).